"Her parents are going out."
Translation:Ihre Eltern gehen aus.
Is something like "Ich gehe heraus" correct?
No. gehen implies movement away, but her indicates movement towards the speaker.
ich gehe hinaus = ich gehe raus would be grammatical but just means "I am going outside" (i.e. I am leaving this building).
It doesn't mean "I am going out" (e.g. to a restaurant or a club). You would use the separable verb ausgehen for that.
I thought we weren't allowed to end the sentence in a preposition. So is the reason we can end in "aus" because it is being used as an adverb in this sentence?
It's because it's a separable prefix, from the verb ausgehen.
Separable prefixes sometimes look like prepositions, e.g. ansehen starts with an- just like an der Wand (at the wall), but in ich sehe dich an, an is not a preposition.